ńňđ. 1
(âńĺăî 2)



Across the Disciplines

Why This Chapter Matters To You
Accounting: You need to understand
how to calculate and analyze operating
and financial leverage and to be familiar
with the tax effects of various capital

Information systems: You need to under-
stand the types of capital and what capital
structure is, because you will provide
and Capital
much of the information needed in man-
agement’s determination of the best capi-
tal structure for the firm.

Management: You need to understand
leverage so that you can magnify returns
for the firm’s owners and to understand
capital structure theory so that you can
make decisions about the firm’s optimal
capital structure.
Marketing: You need to understand
breakeven analysis, which you will use in
pricing and product feasibility decisions.
Discuss the role of breakeven
Operations: You need to understand the LG1
analysis, the operating breakeven
impact of fixed and variable operating
point, and the effect of changing
costs on the firm’s breakeven point and its
costs on it.
operating leverage, because these costs
will have a major impact on the firm’s risk Understand operating, financial, and
and return. total leverage and the relationships
among them.
Describe the types of capital, external
assessment of capital structure, the
capital structure of non-U.S. firms,
and capital structure theory.
Explain the optimal capital structure
using a graphical view of the firm’s
cost-of-capital functions and a zero-
growth valuation model.
Discuss the EBIT–EPS approach to
capital structure.
Review the return and risk of
alternative capital structures, their
linkage to market value, and other
important considerations related to
capital structure.
422 PART 4 Long-Term Financial Decisions

L everage involves the use of fixed costs to magnify returns. Its use in the capital
structure of the firm has the potential to increase its return and risk. Leverage
and capital structure are closely related concepts that are linked to capital budget-
ing decisions through the cost of capital. These concepts can be used to minimize
the firm’s cost of capital and maximize its owners’ wealth. This chapter discusses
leverage and capital-structure concepts and techniques and how the firm can use
them to create the best capital structure.


Leverage results from the use of fixed-cost assets or funds to magnify returns to
Results from the use of fixed-cost the firm’s owners. Generally, increases in leverage result in increased return and
assets or funds to magnify
risk, whereas decreases in leverage result in decreased return and risk. The
returns to the firm’s owners.
amount of leverage in the firm’s capital structure—the mix of long-term debt and
equity maintained by the firm—can significantly affect its value by affecting
capital structure
The mix of long-term debt and return and risk. Unlike some causes of risk, management has almost complete
equity maintained by the firm.
control over the risk introduced through the use of leverage. Because of its effect
on value, the financial manager must understand how to measure and evaluate
leverage, particularly when making capital structure decisions.
The three basic types of leverage can best be defined with reference to the firm’s
income statement, as shown in the general income statement format in Table 11.1.

• Operating leverage is concerned with the relationship between the firm’s
sales revenue and its earnings before interest and taxes, or EBIT. (EBIT is a
descriptive label for operating profits.)
• Financial leverage is concerned with the relationship between the firm’s EBIT
and its common stock earnings per share (EPS).
• Total leverage is concerned with the relationship between the firm’s sales rev-
enue and EPS.

TABLE 11.1 General Income Statement Format and Types
of Leverage
Sales revenue
Less: Cost of goods sold
Operating leverage Gross profits
Less: Operating expenses
Earnings before interest and taxes (EBIT)
Less: Interest
Total leverage
Net profits before taxes
Less: Taxes
Net profits after taxes
Financial leverage
Less: Preferred stock dividends
Earnings available for common stockholders

Earnings per share (EPS)
CHAPTER 11 Leverage and Capital Structure

We will examine the three types of leverage concepts in detail in sections that
follow. First, though, we will look at breakeven analysis, which lays the founda-
tion for leverage concepts by demonstrating the effects of fixed costs on the firm’s

Breakeven Analysis
Breakeven analysis, sometimes called cost-volume-profit analysis, is used by the
breakeven analysis
Indicates the level of operations firm (1) to determine the level of operations necessary to cover all operating costs
necessary to cover all operating
and (2) to evaluate the profitability associated with various levels of sales. The
costs and the profitability associ-
firm’s operating breakeven point is the level of sales necessary to cover all operat-
ated with various levels of sales.
ing costs. At that point, earnings before interest and taxes equals $0.1
operating breakeven point The first step in finding the operating breakeven point is to divide the cost of
The level of sales necessary to
goods sold and operating expenses into fixed and variable operating costs. Fixed
cover all operating costs; the
costs are a function of time, not sales volume, and are typically contractual; rent,
point at which EBIT $0.
for example, is a fixed cost. Variable costs vary directly with sales and are a func-
tion of volume, not time; shipping costs, for example, are a variable cost.2

The Algebraic Approach
Using the following variables, we can recast the operating portion of the firm’s
income statement given in Table 11.1 into the algebraic representation shown in
Table 11.2.
P sale price per unit
Q sales quantity in units
FC fixed operating cost per period
VC variable operating cost per unit
Rewriting the algebraic calculations in Table 11.2 as a formula for earnings
before interest and taxes yields Equation 11.1:

EBIT (P Q) FC (VC Q) (11.1)

TABLE 11.2 Operating Leverage, Costs, and
Breakeven Analysis

Item representation

Sales revenue (P Q)
Less: Fixed operating costs FC
Operating leverage
Less: Variable operating costs (VC Q)
Earnings before interest and taxes EBIT

1. Quite often, the breakeven point is calculated so that it represents the point at which all operating and financial
costs are covered. Our concern in this chapter is not with this overall breakeven point.
2. Some costs, commonly called semifixed or semivariable, are partly fixed and partly variable. An example is sales
commissions that are fixed for a certain volume of sales and then increase to higher levels for higher volumes. For
convenience and clarity, we assume that all costs can be classified as either fixed or variable.
424 PART 4 Long-Term Financial Decisions

Simplifying Equation 11.1 yields

EBIT Q (P VC) FC (11.2)

As noted above, the operating breakeven point is the level of sales at which all
fixed and variable operating costs are covered—the level at which EBIT equals
$0. Setting EBIT equal to $0 and solving Equation 11.2 for Q yield

Q (11.3)

Q is the firm’s operating breakeven point.

Assume that Cheryl’s Posters, a small poster retailer, has fixed operating costs of
$2,500, its sale price per unit (poster) is $10, and its variable operating cost per
unit is $5. Applying Equation 11.3 to these data yields

$2,500 $2,500
Q 500 units
$10 $5 $5

At sales of 500 units, the firm’s EBIT should just equal $0. The firm will have
positive EBIT for sales greater than 500 units and negative EBIT, or a loss, for
sales less than 500 units. We can confirm this by substituting values above and
below 500 units, along with the other values given, into Equation 11.1.

The Graphical Approach
Figure 11.1 presents in graphical form the breakeven analysis of the data in the
preceding example. The firm’s operating breakeven point is the point at which its
total operating cost—the sum of its fixed and variable operating costs—equals
sales revenue. At this point, EBIT equals $0. The figure shows that for sales
below 500 units, total operating cost exceeds sales revenue, and EBIT is less than
$0 (a loss). For sales above the breakeven point of 500 units, sales revenue
exceeds total operating cost, and EBIT is greater than $0.

Changing Costs and the
Operating Breakeven Point
A firm’s operating breakeven point is sensitive to a number of variables: fixed
operating cost (FC), the sale price per unit (P), and the variable operating cost per
unit (VC). The effects of increases or decreases in these variables can be readily
seen by referring to Equation 11.3. The sensitivity of the breakeven sales volume
(Q) to an increase in each of these variables is summarized in Table 11.3. As
might be expected, an increase in cost (FC or VC) tends to increase the operating
breakeven point, whereas an increase in the sale price per unit (P) decreases the
operating breakeven point.

Assume that Cheryl’s Posters wishes to evaluate the impact of several options: (1)
increasing fixed operating costs to $3,000, (2) increasing the sale price per unit to
CHAPTER 11 Leverage and Capital Structure

Breakeven Analysis
Graphical operating
breakeven analysis Total


10,000 Cost

Costs/Revenues ($)

6,000 Operating

0 500 1,000 1,500 2,000 2,500 3,000
Sales (units)

$12.50, (3) increasing the variable operating cost per unit to $7.50, and (4)
simultaneously implementing all three of these changes. Substituting the appro-
priate data into Equation 11.3 yields the following results:

(1) Operating breakeven point 600 units
$10 $5

3331⁄3 units
(2) Operating breakeven point
$12.50 $5

TABLE 11.3 Sensitivity of Operating
Breakeven Point to Increases
in Key Breakeven Variables

Effect on operating
Increase in variable breakeven point

Fixed operating cost (FC) Increase
Sale price per unit (P) Decrease
Variable operating cost per unit (VC) Increase

Note: Decreases in each of the variables shown would have the oppo-
site effect from their effect on operating breakeven point.
426 PART 4 Long-Term Financial Decisions

(3) Operating breakeven point 1,000 units
$10 $7.50
(4) Operating breakeven point 600 units
$12.50 $7.50

Comparing the resulting operating breakeven points to the initial value of 500
units, we can see that the cost increases (actions 1 and 3) raise the breakeven
point, whereas the revenue increase (action 2) lowers the breakeven point. The
combined effect of increasing all three variables (action 4) also results in an
increased operating breakeven point.

We now turn our attention to the three types of leverage. It is important to
recognize that the demonstrations of leverage that follow are conceptual in
nature and that the measures presented are not routinely used by financial man-
agers for decision-making purposes.

Operating Leverage
operating leverage
The potential use of fixed operat- Operating leverage results from the existence of fixed operating costs in the firm’s
ing costs to magnify the effects
income stream. Using the structure presented in Table 11.2, we can define operat-
of changes in sales on the firm’s
ing leverage as the potential use of fixed operating costs to magnify the effects of
earnings before interest and
changes in sales on the firm’s earnings before interest and taxes.

Using the data for Cheryl’s Posters (sale price, P $10 per unit; variable operat-
ing cost, VC $5 per unit; fixed operating cost, FC $2,500), Figure 11.2 pre-
sents the operating breakeven graph originally shown in Figure 11.1. The addi-
tional notations on the graph indicate that as the firm’s sales increase from 1,000
to 1,500 units (Q1 to Q2), its EBIT increases from $2,500 to $5,000 (EBIT1 to
EBIT2). In other words, a 50% increase in sales (1,000 to 1,500 units) results in
a 100% increase in EBIT ($2,500 to $5,000). Table 11.4 includes the data for

TABLE 11.4 The EBIT for Various Sales Levels

Case 2 Case 1

50% 50%

Sales (in units) 500 1,000 1,500

Sales revenuea $5,000 $10,000 $15,000
Less: Variable operating costsb 2,500 5,000 7,500
Less: Fixed operating costs 2,500 2,500 2,500
Earnings before interest and taxes (EBIT) $ 0 $ 2,500 $ 5,000

100% 100%
aSales revenue $10/unit sales in units.
bVariable operating costs $5/unit sales in units.
CHAPTER 11 Leverage and Capital Structure

Operating Leverage Revenue
Breakeven analysis and
operating leverage
14,000 Total

Costs/Revenues ($)
12,000 ($5,000)


2,000 Cost

0 500 1,000 1,500 2,000 2,500 3,000
Q1 Q2
Sales (units)

Figure 11.2 as well as relevant data for a 500-unit sales level. We can illustrate
two cases using the 1,000-unit sales level as a reference point.

Case 1 A 50% increase in sales (from 1,000 to 1,500 units) results in a
100% increase in EBIT (from $2,500 to $5,000).
Case 2 A 50% decrease in sales (from 1,000 to 500 units) results in a 100%
decrease in EBIT (from $2,500 to $0).

From the preceding example, we see that operating leverage works in both
directions. When a firm has fixed operating costs, operating leverage is present.
An increase in sales results in a more-than-proportional increase in EBIT; a
decrease in sales results in a more-than-proportional decrease in EBIT.

Measuring the Degree of Operating Leverage (DOL)
The degree of operating leverage (DOL) is the numerical measure of the firm’s
degree of operating
leverage (DOL) operating leverage. It can be derived using the following equation:3
The numerical measure of the
Percentage change in EBIT
firm’s operating leverage.
DOL (11.4)
Percentage change in sales

3. The degree of operating leverage also depends on the base level of sales used as a point of reference. The closer the
base sales level used is to the operating breakeven point, the greater the operating leverage. Comparison of the
degree of operating leverage of two firms is valid only when the same base level of sales is used for both firms.
428 PART 4 Long-Term Financial Decisions

Whenever the percentage change in EBIT resulting from a given percentage change
in sales is greater than the percentage change in sales, operating leverage exists.
This means that as long as DOL is greater than 1, there is operating leverage.

Applying Equation 11.4 to cases 1 and 2 in Table 11.4 yields the following results:4
Case 1: 2.0
Case 2: 2.0

Because the result is greater than 1, operating leverage exists. For a given base
level of sales, the higher the value resulting from applying Equation 11.4, the
greater the degree of operating leverage.

A more direct formula for calculating the degree of operating leverage at a
base sales level, Q, is shown in Equation 11.5.
Q (P VC)
DOL at base sales level Q (11.5)

Substituting Q 1,000, P $10, VC $5, and FC $2,500 into Equation 11.5
yields the following result:
1,000 ($10 $5) $5,000
DOL at 1,000 units 2.0
1,000 ($10 $5) $2,500 $2,500

The use of the formula results in the same value for DOL (2.0) as that found by
using Table 11.4 and Equation 11.4.5

Fixed Costs and Operating Leverage
Changes in fixed operating costs affect operating leverage significantly. Firms
sometimes can incur fixed operating costs rather than variable operating costs
and at other times may be able to substitute one type of cost for the other. For
example, a firm could make fixed-dollar lease payments rather than payments
equal to a specified percentage of sales. Or it could compensate sales representa-
tives with a fixed salary and bonus rather than on a pure percent-of-sales com-

4. Because the concept of leverage is linear, positive and negative changes of equal magnitude will always result in
equal degrees of leverage when the same base sales level is used as a point of reference. This relationship holds for all
types of leverage discussed in this chapter.
5. When total sales in dollars—instead of unit sales—are available, the following equation, in which TR dollar
level of base sales and TVC total variable operating costs in dollars, can be used.
DOL at base dollar sales TR
This formula is especially useful for finding the DOL for multiproduct firms. It should be clear that because in the
case of a single-product firm, TR P Q and TVC VC Q, substitution of these values into Equation 11.5
results in the equation given here.
CHAPTER 11 Leverage and Capital Structure

TABLE 11.5 Operating Leverage and Increased
Fixed Costs

Case 2 Case 1

50% 50%

Sales (in units) 500 1,000 1,500

Sales revenuea $5,000 $10,000 $15,000
Less: Variable operating 2,250 4,500 6,750
Less: Fixed operating costs 3,000 3,000 3,000
Earnings before interest and taxes (EBIT) $ 250 $ 2,500 $ 5,250

110% 110%
aSales revenue was calculated as indicated in Table 11.4.
bVariable operating costs $4.50/unit sales in units.

mission basis. The effects of changes in fixed operating costs on operating lever-
age can best be illustrated by continuing our example.

Assume that Cheryl’s Posters exchanges a portion of its variable operating costs
for fixed operating costs by eliminating sales commissions and increasing sales
salaries. This exchange results in a reduction in the variable operating cost per
unit from $5 to $4.50 and an increase in the fixed operating costs from $2,500 to
$3,000. Table 11.5 presents an analysis like that in Table 11.4, but using the new
costs. Although the EBIT of $2,500 at the 1,000-unit sales level is the same as
before the shift in operating cost structure, Table 11.5 shows that the firm has
increased its operating leverage by shifting to greater fixed operating costs.
With the substitution of the appropriate values into Equation 11.5, the
degree of operating leverage at the 1,000-unit base level of sales becomes

1,000 ($10 $4.50) $5,500
DOL at 1,000 units 2.2
1,000 ($10 $4.50) $3,000 $2,500

Comparing this value to the DOL of 2.0 before the shift to more fixed costs
makes it is clear that the higher the firm’s fixed operating costs relative to vari-
able operating costs, the greater the degree of operating leverage.

Financial Leverage
financial leverage Financial leverage results from the presence of fixed financial costs in the firm’s
The potential use of fixed income stream. Using the framework in Table 11.1, we can define financial
financial costs to magnify the
leverage as the potential use of fixed financial costs to magnify the effects of
effects of changes in earnings
changes in earnings before interest and taxes on the firm’s earnings per share.
before interest and taxes on the
The two fixed financial costs that may be found on the firm’s income statement
firm’s earnings per share.
430 PART 4 Long-Term Financial Decisions

are (1) interest on debt and (2) preferred stock dividends. These charges must be
paid regardless of the amount of EBIT available to pay them.6

Chen Foods, a small Oriental food company, expects EBIT of $10,000 in the cur-
rent year. It has a $20,000 bond with a 10% (annual) coupon rate of interest and
an issue of 600 shares of $4 (annual dividend per share) preferred stock outstand-
ing. It also has 1,000 shares of common stock outstanding. The annual interest
on the bond issue is $2,000 (0.10 $20,000). The annual dividends on the pre-
ferred stock are $2,400 ($4.00/share 600 shares). Table 11.6 presents the EPS
corresponding to levels of EBIT of $6,000, $10,000, and $14,000, assuming that
the firm is in the 40% tax bracket. Two situations are shown:
Case 1 A 40% increase in EBIT (from $10,000 to $14,000) results in a
100% increase in earnings per share (from $2.40 to $4.80).
Case 2 A 40% decrease in EBIT (from $10,000 to $6,000) results in a
100% decrease in earnings per share (from $2.40 to $0).

The effect of financial leverage is such that an increase in the firm’s EBIT
results in a more-than-proportional increase in the firm’s earnings per share,
whereas a decrease in the firm’s EBIT results in a more-than-proportional
decrease in EPS.

The EPS for Various EBIT Levelsa
TABLE 11.6

Case 2 Case 1

40% 40%

EBIT $6,000 $10,000 $14,000
Less: Interest (I) 2,000 2,000 2,000
Net profits before taxes $4,000 $ 8,000 $12,000
Less: Taxes (T 0.40) 1,600 3,200 4,800
Net profits after taxes $2,400 $ 4,800 $ 7,200
Less: Preferred stock dividends (PD) 2,400 2,400 2,400
Earnings available for common (EAC) $ 0 $ 2,400 $ 4,800

$0 $2,400 $4,800
Earnings per share (EPS) $0 $2.40 $4.80
1,000 1,000 1,000

100% 100%
aAsnoted in Chapter 1, for accounting and tax purposes, interest is a tax-deductible expense, whereas divi-
dends must be paid from after-tax cash flows.

6. As noted in Chapter 7, although preferred stock dividends can be “passed” (not paid) at the option of the firm’s
directors, it is generally believed that payment of such dividends is necessary. This text treats the preferred stock div-
idend as a contractual obligation, not only to be paid as a fixed amount, but also to be paid as scheduled. Although
failure to pay preferred dividends cannot force the firm into bankruptcy, it increases the common stockholders’ risk
because they cannot be paid dividends until the claims of preferred stockholders are satisfied.
CHAPTER 11 Leverage and Capital Structure

Measuring the Degree of Financial Leverage (DFL)
The degree of financial leverage (DFL) is the numerical measure of the firm’s
degree of financial leverage
(DFL) financial leverage. Computing it is much like computing the degree of operating
The numerical measure of the
leverage. The following equation presents one approach for obtaining the DFL.7
firm’s financial leverage.
Percentage change in EPS
DFL (11.6)
Percentage change in EBIT

Whenever the percentage change in EPS resulting from a given percentage change
in EBIT is greater than the percentage change in EBIT, financial leverage exists.
This means that whenever DFL is greater than 1, there is financial leverage.

Applying Equation 11.6 to cases 1 and 2 in Table 11.6 yields
Case 1: 2.5
Case 2: 2.5

In both cases, the quotient is greater than 1, so financial leverage exists. The
higher this value, the greater the degree of financial leverage.

A more direct formula for calculating the degree of financial leverage at a
base level of EBIT is given by Equation 11.7, where the notation from Table 11.6
is used. Note that in the denominator, the term 1/(1 T) converts the after-tax
preferred stock dividend to a before-tax amount for consistency with the other
terms in the equation.

DFL at base level EBIT (11.7)
1 T

Substituting EBIT $10,000, I $2,000, PD $2,400, and the tax rate (T
0.40) into Equation 11.7 yields the following result:

DFL at $10,000 EBIT
$10,000 $2,000 $2,400
1 0.40

Note that the formula given in Equation 11.7 provides a more direct method
for calculating the degree of financial leverage than the approach illustrated using
Table 11.6 and Equation 11.6.

7. This approach is valid only when the same base level of EBIT is used to calculate and compare these values. In
other words, the base level of EBIT must be held constant to compare the financial leverage associated with different
levels of fixed financial costs.
432 PART 4 Long-Term Financial Decisions

Total Leverage
We also can assess the combined effect of operating and financial leverage on the
firm’s risk by using a framework similar to that used to develop the individual
concepts of leverage. This combined effect, or total leverage, can be defined as the
total leverage
The potential use of fixed costs, potential use of fixed costs, both operating and financial, to magnify the effect of
both operating and financial, to changes in sales on the firm’s earnings per share. Total leverage can therefore be
magnify the effect of changes in
viewed as the total impact of the fixed costs in the firm’s operating and financial
sales on the firm’s earnings per

Cables Inc., a computer cable manufacturer, expects sales of 20,000 units at $5
per unit in the coming year and must meet the following obligations: variable
operating costs of $2 per unit, fixed operating costs of $10,000, interest of
$20,000, and preferred stock dividends of $12,000. The firm is in the 40% tax
bracket and has 5,000 shares of common stock outstanding. Table 11.7 presents
the levels of earnings per share associated with the expected sales of 20,000 units
and with sales of 30,000 units.
The table illustrates that as a result of a 50% increase in sales (from 20,000
to 30,000 units), the firm would experience a 300% increase in earnings per
share (from $1.20 to $4.80). Although it is not shown in the table, a 50%
decrease in sales would, conversely, result in a 300% decrease in earnings per
share. The linear nature of the leverage relationship accounts for the fact that

TABLE 11.7 The Total Leverage Effect


Sales (in units) 20,000 30,000

Sales revenuea $100,000 $150,000
Less: Variable operating 40,000 60,000 DOL 1.2
Less: Fixed operating costs 10,000 10,000
Earnings before interest and
taxes (EBIT) $ 50,000 $ 80,000

DTL 6.0
Less: Interest 20,000 20,000
Net profits before taxes $ 30,000 $ 60,000
DFL 5.0
Less: Taxes (T 0.40) 12,000 24,000 60%
Net profits after taxes $ 18,000 $ 36,000
Less: Preferred stock dividends 12,000 12,000
Earnings available for common $ 6,000 $ 24,000

$6,000 $24,000
Earnings per share (EPS) $1.20 $4.80
5,000 5,000

aSales revenue $5/unit sales in units.
bVariable operating costs $2/unit sales in units.
CHAPTER 11 Leverage and Capital Structure

sales changes of equal magnitude in opposite directions result in EPS changes of
equal magnitude in the corresponding direction. At this point, it should be clear
that whenever a firm has fixed costs—operating or financial—in its structure,
total leverage will exist.

Measuring the Degree of Total Leverage (DTL)
The degree of total leverage (DTL) is the numerical measure of the firm’s total
degree of total leverage (DTL)
The numerical measure of the leverage. It can be computed much as operating and financial leverage are com-
firm’s total leverage. puted. The following equation presents one approach for measuring DTL:8
Percentage change in EPS
DTL (11.8)
Percentage change in sales
Whenever the percentage change in EPS resulting from a given percentage change
in sales is greater than the percentage change in sales, total leverage exists. This
means that as long as the DTL is greater than 1, there is total leverage.

Applying Equation 11.8 to the data in Table 11.7 yields
DTL 6.0
Because this result is greater than 1, total leverage exists. The higher the value,
the greater the degree of total leverage.

A more direct formula for calculating the degree of total leverage at a given
base level of sales, Q, is given by Equation 11.9, which uses the same notation
that was presented earlier:
Q (P VC)
DTL at base sales level Q (11.9)
1 T

Substituting Q 20,000, P $5, VC $2, FC $10,000, I $20,000, PD
$12,000, and the tax rate (T 0.40) into Equation 11.9 yields
DTL at 20,000 units
20,000 ($5 $2)
20,000 ($5 $2) $10,000 $20,000 $12,000
1 0.40
Clearly, the formula used in Equation 11.9 provides a more direct method for
calculating the degree of total leverage than the approach illustrated using Table
11.7 and Equation 11.8.

8. This approach is valid only when the same base level of sales is used to calculate and compare these values. In
other words, the base level of sales must be held constant if we are to compare the total leverage associated with dif-
ferent levels of fixed costs.
434 PART 4 Long-Term Financial Decisions

The Relationship of Operating, Financial, and Total Leverage
Total leverage reflects the combined impact of operating and financial leverage
on the firm. High operating leverage and high financial leverage will cause total
leverage to be high. The opposite will also be true. The relationship between oper-
ating leverage and financial leverage is multiplicative rather than additive. The
relationship between the degree of total leverage (DTL) and the degrees of operat-
ing leverage (DOL) and financial leverage (DFL) is given by Equation 11.10.
DTL DOL DFL (11.10)

Substituting the values calculated for DOL and DFL, shown on the right-hand
side of Table 11.7, into Equation 11.10 yields
DTL 1.2 5.0 6.0
The resulting degree of total leverage is the same value that we calculated directly
in the preceding examples.

Review Questions

11–1 What is meant by the term leverage? How are operating leverage, financial
leverage, and total leverage related to the income statement?
11–2 What is the operating breakeven point? How do changes in fixed operat-
ing costs, the sale price per unit, and the variable operating cost per unit
affect it?
11–3 What is operating leverage? What causes it? How is the degree of operat-
ing leverage (DOL) measured?
11–4 What is financial leverage? What causes it? How is the degree of financial
leverage (DFL) measured?
11–5 What is the general relationship among operating leverage, financial lever-
age, and the total leverage of the firm? Do these types of leverage comple-
ment each other? Why or why not?

The Firm’s Capital Structure

Capital structure is one of the most complex areas of financial decision making
because of its interrelationship with other financial decision variables.9 Poor cap-
ital structure decisions can result in a high cost of capital, thereby lowering the
NPVs of projects and making more of them unacceptable. Effective capital struc-
ture decisions can lower the cost of capital, resulting in higher NPVs and more
acceptable projects—and thereby increasing the value of the firm. This section
links together many of the concepts presented in Chapters 4, 5, 6, 7, and 10 and
the discussion of leverage in this chapter.

9. Of course, although capital structure is financially important, it, like many business decisions, is generally not so
important as the firm’s products or services. In a practical sense, a firm can probably more readily increase its value
by improving quality and reducing costs than by fine-tuning its capital structure.
CHAPTER 11 Leverage and Capital Structure

Types of Capital
All of the items on the right-hand side of the firm’s balance sheet, excluding cur-
rent liabilities, are sources of capital. The following simplified balance sheet illus-
trates the basic breakdown of total capital into its two components, debt capital
and equity capital.

Balance Sheet

Current liabilities
Long-term debt capital

Assets Stockholders’ equity
Preferred stock capital
Common stock equity capital
Common stock
Retained earnings

The various types and characteristics of corporate bonds, a major source of
debt capital, were discussed in detail in Chapter 6. The cost of debt is lower than
the cost of other forms of financing. Lenders demand relatively lower returns
because they take the least risk of any long-term contributors of capital: (1) They
have a higher priority of claim against any earnings or assets available for pay-
ment. (2) They can exert far greater legal pressure against the company to make
payment than can holders of preferred or common stock. (3) The tax deductibil-
ity of interest payments lowers the debt cost to the firm substantially.
Unlike debt capital, which must be repaid at some future date, equity capital
is expected to remain in the firm for an indefinite period of time. The two basic
sources of equity capital are (1) preferred stock and (2) common stock equity,
which includes common stock and retained earnings. Common stock is typically
the most expensive form of equity, followed by retained earnings and then pre-
ferred stock. Our concern here is the relationship between debt and equity capital.
Key differences between these two types of capital, relative to voice in manage-
ment, claims on income and assets, maturity, and tax treatment, were summarized
in Chapter 7, Table 7.1. Because of its secondary position relative to debt, suppli-
ers of equity capital take greater risk than suppliers of debt capital and therefore
must be compensated with higher expected returns.

External Assessment of Capital Structure
We saw earlier that financial leverage results from the use of fixed-cost financing,
such as debt and preferred stock, to magnify return and risk. The amount of lever-
age in the firm’s capital structure can affect its value by affecting return and risk.
Those outside the firm can make a rough assessment of capital structure by using
measures found in the firm’s financial statements. Some of these important debt
ratios were presented in Chapter 2. For example, a direct measure of the degree of
436 PART 4 Long-Term Financial Decisions

indebtedness is the debt ratio. The higher this ratio, the greater the relative
amount of debt (or financial leverage) in the firm’s capital structure. Measures of
the firm’s ability to meet contractual payments associated with debt include the
times interest earned ratio and the fixed-payment coverage ratio. These ratios
provide indirect information on financial leverage. Generally, the smaller these
ratios, the greater the firm’s financial leverage and the less able it is to meet pay-
ments as they come due.
The level of debt (financial leverage) that is acceptable for one industry or
line of business can be highly risky in another, because different industries and
lines of business have different operating characteristics. Table 11.8 presents the
debt and times interest earned ratios for selected industries and lines of business.
Significant industry differences can be seen in these data. Differences in debt posi-
tions are also likely to exist within an industry or line of business.

TABLE 11.8 Debt Ratios for Selected Industries and
Lines of Business (Fiscal Years Ended
4/1/00 Through 3/31/01)

Times interest
Industry or line of business Debt ratio earned ratio

Manufacturing industries
Books 65.2% 3.3
Dairy products 74.6 3.0
Electronic computers 55.4 3.4
Iron and steel forgings 62.7 2.3
Machine tools, metal cutting types 60.4 2.4
Wines & distilled alcoholic beverages 69.7 4.4
Women’s, misses’ & juniors’ dresses 53.5 2.4
Wholesaling industries
Furniture 69.4 3.0
General groceries 66.8 2.8
Men’s and boys’ clothing 60.8 2.6
Retailing industries
Autos, new and used 76.1 1.4
Department stores 52.8 2.3
Restaurants 92.5 2.3
Service industries
Accounting, auditing, bookkeeping 68.4 5.6
Advertising agencies 81.3 4.2
Auto repair—general 75.9 2.5
Insurance agents and brokers 94.1 4.1

Source: RMA Annual Statement Studies, 2001–2002 (fiscal years ended 4/1/00 through
3/31/01) (Philadelphia: Robert Morris Associates, 2001). Copyright © 2001 by Robert Morris
Note: Robert Morris Associates recommends that these ratios be regarded only as general
guidelines and not as absolute industry norms. No claim is made as to the representativeness of
these figures.
CHAPTER 11 Leverage and Capital Structure

In Practice
FOCUS ON PRACTICE Enron Plays Hide and Seek with Debt
Enron Corp.’s December 31, 2000, that Enron was not liable for repay- lines have large aircraft leases
balance sheet showed long-term ment of the debts of these SPEs. structured through off-balance-
debt of $10. 2 billion and $300 mil- Enron’s required filing of Form sheet vehicles, although analysts
lion in other financial obligations. 10-Q with the SEC, on November and investors are aware that the
These figures gave the company a 19, 2001, told a different story: If its true leverage is higher. Pacific Gas
41 percent ratio of total obliga- debt were to fall below investment & Electric, Southern California
tions to total capitalization. That grade, Enron would have to repay Edison, and Xerox have also run
didn’t seem out of line for a com- those off-balance-sheet partner- into problems from off-balance-
pany in the capital-intensive ship obligations. Ironically, its dis- sheet debt obligations. Don’t
energy industry. closure of about $4 billion in off- expect the Enron debacle to elimi-
Yet as the company’s finan- balance-sheet liabilities triggered nate special-purpose entities,
cial condition fell apart in the fall of the downgrade of its debt to “junk” although the SEC has been calling
2001, investors and lenders discov- status and accelerated debt for tighter consolidation rules.
ered that Enron’s true debt load repayment. Enron’s secrecy about Companies like the flexibility that
was far beyond what its balance its off-balance-sheet ventures led off-balance-sheet financing
sheet indicated. By selling assets to its loss of credibility in the sources provide, not to mention
to perfectly legal special-purpose investment community. Its stock that such financing makes debt
entities (SPEs), Enron had moved and bond prices slid downward; its ratios and returns look better.
billions of dollars of debt off its bal- market value plunged $35 billion in
ance sheet into subsidiaries, about a month; and on December Sources: Peter Behr, “Cause of Death: Mis-
trusts, partnerships, and other cre- 2, 2001, Enron became the largest trust,” Washington Post (December 13, 2001),
p. E1; Ronald Fink, “What Andrew Fastow
ative financing arrangements. For- U.S. company ever to have filed for
Knew,” CFO (January 1, 2002); and David
mer CFO Andrew Fastow claimed bankruptcy. Henry, “Who Else Is Hiding Debt?” Business
that these complex arrangements Enron is not alone in its use of Week (January 28, 2002).
were disclosed in footnotes and off-balance-sheet debt. Most air-

Capital Structure of Non-U.S. Firms
In general, non-U.S. companies have much higher degrees of indebtedness than
their U.S. counterparts. Most of the reasons for this are related to the fact that
U.S. capital markets are much more developed than those elsewhere and have
played a greater role in corporate financing than has been the case in other
countries. In most European countries and especially in Japan and other Pacific
Rim nations, large commercial banks are more actively involved in the financing
of corporate activity than has been true in the United States. Furthermore, in
many of these countries, banks are allowed to make large equity investments in
nonfinancial corporations—a practice that is prohibited for U.S. banks. Finally,
share ownership tends to be more tightly controlled among founding-family,
institutional, and even public investors in Europe and Asia than it is for most
large U.S. corporations. Tight ownership enables owners to understand the
firm’s financial condition better, resulting in their willingness to tolerate a higher
degree of indebtedness.
On the other hand, similarities do exist between U.S. corporations and cor-
porations in other countries. First, the same industry patterns of capital structure
tend to be found all around the world. For example, in nearly all countries, phar-
maceutical and other high-growth industrial firms tend to have lower debt ratios
438 PART 4 Long-Term Financial Decisions

than do steel companies, airlines, and electric utility companies. Second, the capi-
tal structures of the largest U.S.-based multinational companies, which have
access to many different capital markets around the world, typically resemble the
capital structures of multinational companies from other countries more than
they resemble those of smaller U.S. companies. Finally, the worldwide trend is
away from reliance on banks for corporate financing and toward greater reliance
on security issuance. Over time, the differences in the capital structures of U.S.
and non-U.S. firms will probably lessen.

Capital Structure Theory
Scholarly research suggests that there is an optimal capital structure range. It is
not yet possible to provide financial managers with a specified methodology for
use in determining a firm’s optimal capital structure. Nevertheless, financial the-
ory does offer help in understanding how a firm’s chosen financing mix affects
the firm’s value.
In 1958, Franco Modigliani and Merton H. Miller10 (commonly known as
“M and M”) demonstrated algebraically that, assuming perfect markets,11 the
capital structure that a firm chooses does not affect its value. Many researchers,
including M and M, have examined the effects of less restrictive assumptions on
the relationship between capital structure and the firm’s value. The result is a the-
oretical optimal capital structure based on balancing the benefits and costs of
debt financing. The major benefit of debt financing is the tax shield, which allows
interest payments to be deducted in calculating taxable income. The cost of debt
financing results from (1) the increased probability of bankruptcy caused by debt
obligations, (2) the agency costs of the lender’s monitoring the firm’s actions, and
(3) the costs associated with managers having more information about the firm’s
prospects than do investors.

Tax Benefits
Allowing firms to deduct interest payments on debt when calculating taxable
income reduces the amount of the firm’s earnings paid in taxes, thereby making
more earnings available for bondholders and stockholders. The deductibility of
interest means the cost of debt, ki, to the firm is subsidized by the government.
Letting kd equal the before-tax cost of debt and letting T equal the tax rate, from
Chapter 10 (Equation 10.2), we have ki kd (1 T).

Probability of Bankruptcy
The chance that a firm will become bankrupt because of an inability to meet its
obligations as they come due depends largely on its level of both business risk and
financial risk.

10. Franco Modigliani and Merton H. Miller, “The Cost of Capital, Corporation Finance, and the Theory of Invest-
ment,” American Economic Review (June 1958), pp. 261–297.
11. Perfect-market assumptions include (1) no taxes, (2) no brokerage or flotation costs for securities, (3) symmetri-
cal information—investors and managers have the same information about the firm’s investment prospects, and (4)
investor ability to borrow at the same rate as corporations.
CHAPTER 11 Leverage and Capital Structure

Business Risk In Chapter 10, we defined business risk as the risk to the firm
of being unable to cover its operating costs. In general, the greater the firm’s
operating leverage—the use of fixed operating costs—the higher its business risk.
Although operating leverage is an important factor affecting business risk, two
other factors—revenue stability and cost stability—also affect it. Revenue stabil-
ity reflects the relative variability of the firm’s sales revenues. Firms with reason-
ably stable levels of demand and with products that have stable prices have stable
revenues. The result is low levels of business risk. Firms with highly volatile prod-
uct demand and prices have unstable revenues that result in high levels of busi-
ness risk. Cost stability reflects the relative predictability of input prices such as
those for labor and materials. The more predictable and stable these input prices
are, the lower the business risk; the less predictable and stable they are, the higher
the business risk.
Business risk varies among firms, regardless of their lines of business, and is
not affected by capital structure decisions. The level of business risk must be
taken as a “given.” The higher a firm’s business risk, the more cautious the firm
must be in establishing its capital structure. Firms with high business risk there-
fore tend toward less highly leveraged capital structures, and firms with low busi-
ness risk tend toward more highly leveraged capital structures. We will hold
business risk constant throughout the discussions that follow.

Financial Risk The firm’s capital structure directly affects its financial
risk, which is the risk to the firm of being unable to cover required financial
obligations. The penalty for not meeting financial obligations is bankruptcy. The
more fixed-cost financing—debt (including financial leases) and preferred
stock—a firm has in its capital structure, the greater its financial leverage and
risk. Financial risk depends on the capital structure decision made by the man-
agement, and that decision is affected by the business risk the firm faces. The
total risk of a firm—business and financial risk combined—determines its prob-
ability of bankruptcy.

Agency Costs Imposed by Lenders
As noted in Chapter 1, the managers of firms typically act as agents of the owners
(stockholders). The owners give the managers the authority to manage the firm
for the owners’ benefit. The agency problem created by this relationship extends
not only to the relationship between owners and managers but also to the rela-
tionship between owners and lenders.
When a lender provides funds to a firm, the interest rate charged is based on
the lender’s assessment of the firm’s risk. The lender–borrower relationship,
therefore, depends on the lender’s expectations for the firm’s subsequent behav-
ior. The borrowing rates are, in effect, locked in when the loans are negotiated.
After obtaining a loan at a certain rate, the firm could increase its risk by invest-
ing in risky projects or by incurring additional debt. Such action could weaken
the lender’s position in terms of its claim on the cash flow of the firm. From
another point of view, if these risky investment strategies paid off, the stockhold-
ers would benefit. Because payment obligations to the lender remain unchanged,
the excess cash flows generated by a positive outcome from the riskier action
would enhance the value of the firm to its owners. In other words, if the risky
440 PART 4 Long-Term Financial Decisions

investments pay off, the owners receive all the benefits; but if the risky invest-
ments do not pay off, the lenders share in the costs.
Clearly, an incentive exists for the managers acting on behalf of the stockhold-
ers to “take advantage” of lenders. To avoid this situation, lenders impose certain
monitoring techniques on borrowers, who as a result incur agency costs. The most
obvious strategy is to deny subsequent loan requests or to increase the cost of future
loans to the firm. Because this strategy is an after-the-fact approach, other controls
must be included in the loan agreement. Lenders typically protect themselves by
including provisions that limit the firm’s ability to alter significantly its business and
financial risk. These loan provisions tend to center on issues such as the minimum
level of liquidity, asset acquisitions, executive salaries, and dividend payments.
By including appropriate provisions in the loan agreement, the lender can
control the firm’s risk and thus protect itself against the adverse consequences of
this agency problem. Of course, in exchange for incurring agency costs by agree-
ing to the operating and financial constraints placed on it by the loan provisions,
the firm should benefit by obtaining funds at a lower cost.

Asymmetric Information
Two surveys examined capital structure decisions.12 Financial executives were
asked which of two major criteria determined their financing decisions: (1) main-
taining a target capital structure or (2) following a hierarchy of financing. This
hierarchy, called a pecking order, begins with retained earnings, which is followed
pecking order
A hierarchy of financing that by debt financing and finally external equity financing. Respondents from 31 per-
begins with retained earnings, cent of Fortune 500 firms and from 11 percent of the (smaller) 500 largest over-
which is followed by debt financ-
the-counter firms answered target capital structure. Respondents from 69 percent
ing and finally external equity
of the Fortune 500 firms and 89 percent of the 500 largest OTC firms chose the
pecking order.
At first glance, on the basis of financial theory, this choice appears to be
inconsistent with wealth maximization goals, but Stewart Myers has explained
how “asymmetric information” could account for the pecking order financing
preferences of financial managers.13 Asymmetric information results when man-
asymmetric information
agers of a firm have more information about operations and future prospects
The situation in which managers
of a firm have more information than do investors. Assuming that managers make decisions with the goal of max-
about operations and future
imizing the wealth of existing stockholders, then asymmetric information can
prospects than do investors.
affect the capital structure decisions that managers make.
Suppose, for example, that management has found a valuable investment
that will require additional financing. Management believes that the prospects for
the firm’s future are very good and that the market, as indicated by the firm’s cur-
rent stock price, does not fully appreciate the firm’s value. In this case, it would
be advantageous to current stockholders if management raised the required funds
using debt rather than issuing new stock. Using debt to raise funds is frequently

12. The results of the survey of Fortune 500 firms are reported in J. Michael Pinegar and Lisa Wilbricht, “What
Managers Think of Capital Structure Theory: A Survey,” Financial Management (Winter 1989), pp. 82–91, and the
results of a similar survey of the 500 largest OTC firms are reported in Linda C. Hittle, Kamal Haddad, and
Lawrence J. Gitman, “Over-the-Counter Firms, Asymmetric Information, and Financing Preferences,” Review of
Financial Economics (Fall 1992), pp. 81–92.
13. Stewart C. Myers, “The Capital Structure Puzzle,” Journal of Finance (July 1984), pp. 575–592.
CHAPTER 11 Leverage and Capital Structure

viewed as a signal that reflects management’s view of the firm’s stock value. Debt
A financing action by manage- financing is a positive signal suggesting that management believes that the stock
ment that is believed to reflect its is “undervalued” and therefore a bargain. When the firm’s positive future out-
view of the firm’s stock value;
look becomes known to the market, the increased value will be fully captured by
generally, debt financing is
existing owners, rather than having to be shared with new stockholders.
viewed as a positive signal that
If, however, the outlook for the firm is poor, management may believe that
management believes the stock
is “undervalued,” and a stock the firm’s stock is “overvalued.” In that case, it would be in the best interest of
issue is viewed as a negative existing stockholders for the firm to issue new stock. Therefore, investors often
signal that management believes
interpret the announcement of a stock issue as a negative signal—bad news con-
the stock is “overvalued.”
cerning the firm’s prospects—and the stock price declines. This decrease in stock
value, along with high underwriting costs for stock issues (compared to debt
issues), make new stock financing very expensive. When the negative future out-
look becomes known to the market, the decreased value is shared with new
stockholders, rather than being fully captured by existing owners.
Because conditions of asymmetric information exist from time to time, firms
should maintain some reserve borrowing capacity by keeping debt levels low.
This reserve allows the firm to take advantage of good investment opportunities
without having to sell stock at a low value and thus send signals that unduly
influence the stock price.

The Optimal Capital Structure
What, then, is an optimal capital structure, even if it exists (so far) only in theory?
To provide some insight into an answer, we will examine some basic financial
relationships. It is generally believed that the value of the firm is maximized when
the cost of capital is minimized. By using a modification of the simple zero-
growth valuation model (see Equation 7.2 in Chapter 7), we can define the value
of the firm, V, by Equation 11.11.
EBIT (1 T)
V (11.11)
EBIT earnings before interest and taxes
T tax rate
EBIT (1 T) the after-tax operating earnings available to the debt and
equity holders
ka weighted average cost of capital
Clearly, if we assume that EBIT is constant, the value of the firm, V, is maximized
by minimizing the weighted average cost of capital, ka.

Cost Functions
Figure 11.3(a) plots three cost functions—the cost of debt, the cost of equity, and
the weighted average cost of capital (WACC)—as a function of financial leverage
measured by the debt ratio (debt to total assets). The cost of debt, ki , remains low
because of the tax shield, but it slowly increases as leverage increases, to compen-
sate lenders for increasing risk. The cost of equity, ks, is above the cost of debt. It
442 PART 4 Long-Term Financial Decisions

Cost Functions
and Value
Capital costs and the optimal

capital structure (b)
EBIT Ă— (1 – T)

ks = cost of equity

Annual Cost (%)
ka = WACC
ki = cost of debt

0 Debt/Total Assets
M = Optimal Capital Structure
Financial Leverage

increases as financial leverage increases, but it generally increases more rapidly
than the cost of debt. The cost of equity rises because the stockholders require a
higher return as leverage increases, to compensate for the higher degree of finan-
cial risk.
The weighted average cost of capital (WACC) results from a weighted aver-
age of the firm’s debt and equity capital costs. At a debt ratio of zero, the firm is
100 percent equity-financed. As debt is substituted for equity and as the debt
ratio increases, the WACC declines because the debt cost is less than the equity
cost (ki ks). As the debt ratio continues to increase, the increased debt and
equity costs eventually cause the WACC to rise (after point M in Figure 11.3(a)).
This behavior results in a U-shaped, or saucer-shaped, weighted average cost-of-
capital function, ka.

A Graphical View of the Optimal Structure
Because the maximization of value, V, is achieved when the overall cost of capi-
tal, ka, is at a minimum (see Equation 11.11), the optimal capital structure is that
optimal capital structure
The capital structure at which at which the weighted average cost of capital, ka, is minimized. In Figure 11.3(a),
the weighted average cost of
point M represents the minimum weighted average cost of capital—the point of
capital is minimized, thereby
optimal financial leverage and hence of optimal capital structure for the firm. Fig-
maximizing the firm’s value.
ure 11.3(b) plots the value of the firm that results from substitution of ka in Fig-
ure 11.3(a) for various levels of financial leverage into the zero-growth valuation
model in Equation 11.11. As shown in Figure 11.3(b), at the optimal capital
structure, point M, the value of the firm is maximized at V*.
CHAPTER 11 Leverage and Capital Structure

Generally, the lower the firm’s weighted average cost of capital, the greater
the difference between the return on a project and the WACC, and therefore the
greater the owners’ return. Simply stated, minimizing the weighted average cost
of capital allows management to undertake a larger number of profitable proj-
ects, thereby further increasing the value of the firm.
As a practical matter, there is no way to calculate the optimal capital struc-
ture implied by Figure 11.3. Because it is impossible either to know or to remain
at the precise optimal capital structure, firms generally try to operate in a range
that places them near what they believe to be the optimal capital structure.

Review Questions

11–6 What is a firm’s capital structure? What ratios assess the degree of finan-
cial leverage in a firm’s capital structure?
11–7 In what ways are the capital structures of U.S. and non-U.S. firms differ-
ent? How are they similar?
11–8 What is the major benefit of debt financing? How does it affect the firm’s
cost of debt?
11–9 What are business risk and financial risk? How does each of them influ-
ence the firm’s capital structure decisions?
11–10 Briefly describe the agency problem that exists between owners and
lenders. How do lenders cause firms to incur agency costs to resolve this
11–11 How does asymmetric information affect the firm’s capital structure deci-
sions? How do the firm’s financing actions give investors signals that
reflect management’s view of stock value?
11–12 How do the cost of debt, the cost of equity, and the weighted average cost
of capital (WACC) behave as the firm’s financial leverage increases from
zero? Where is the optimal capital structure? What is its relationship to
the firm’s value at that point?

The EBIT–EPS Approach to Capital Structure

One of the key variables affecting the market value of the firm’s shares is its
EBIT–EPS approach return to owners, as reflected by the firm’s earnings. Therefore, earnings per
An approach for selecting the
share (EPS) can be conveniently used to analyze alternative capital structures.
capital structure that maximizes
The EBIT–EPS approach to capital structure involves selecting the capital struc-
earnings per share (EPS) over the
ture that maximizes EPS over the expected range of earnings before interest and
expected range of earnings
taxes (EBIT).
before interest and taxes (EBIT).

Presenting a Financing Plan Graphically
To analyze the effects of a firm’s capital structure on the owners’ returns, we
consider the relationship between earnings before interest and taxes (EBIT) and
earnings per share (EPS). A constant level of EBIT—constant business risk—is
444 PART 4 Long-Term Financial Decisions

assumed, to isolate the effect on returns of the financing costs associated with
alternative capital structures. EPS is used to measure the owners’ returns, which
are expected to be closely related to share price.

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